Solve y=psinp+cosp

$$y = p \sin p + \cos p$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{\cos(p)-y}{p\psi }\text{, }&p\neq 0\text{ and }\psi \neq 0\\n\in \mathrm{R}\text{, }&\left(y=1\text{ and }p=0\right)\text{ or }\left(y=\cos(p)\text{ and }\psi =0\text{ and }p\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\psi np+\cos(p)=y$$

Subtract \cos(p) from both sides.

$$\psi np=y-\cos(p)$$

The equation is in standard form.

$$p\psi n=-\cos(p)+y$$

Divide both sides by \psi p.

$$\frac{p\psi n}{p\psi }=\frac{-\cos(p)+y}{p\psi }$$

Dividing by \psi p undoes the multiplication by \psi p.

$$n=\frac{-\cos(p)+y}{p\psi }$$